clear all
close all

% u^2 + v^2 = 1
% major radius a
% minor radius b
% coordinates (bu, av)
u=[0:0.01:1];
v=sqrt(1-u.^2);
a=5;
b=2;
x=a*v;
y=b*u;

% how much to offset
% presumably the radius of the tool
T=0.33;

hold on


axis([0 6 0 6])
dt=0.05
t=[0:dt:pi/2+dt];
px=a*cos(t);
py=b*sin(t);
plot(px,py,'m')

nox=b*cos(t);
noy=a*sin(t);
l=sqrt(nox.^2 + noy.^2);
nox=(nox./l)*T;
noy=(noy./l)*T;

plot(px+nox,py+noy)

k=3.4;
plot([k k],[0 6],'k--')

tk=fzero(@oe,[0, pi/2])
    
l=sqrt( (b*cos(tk))^2  + (a*sin(tk))^2 )
ox=(a+T*b/l)*cos(tk)
oy=(b+T*a/l)*sin(tk)
plot(ox,oy,'ko')

px=a*cos(tk);
py=b*sin(tk);
plot(px,py,'*')
h=line([0 px],[0 py])
set(h,'Color','red')
h=line([px ox],[py oy])
set(h,'Color','green')
hold off